Mean-field games (MFGs) are a relatively recent theoretical framework for studying strategic environments with a large number of weakly coupled decision-making agents [1]}, [2]}, [3]}, [4]}, [5]}. In a MFG, the cost and state dynamics of any particular agent are influenced by the collective behaviour of others only through a distributional mean-field term. Mean-field games can be viewed as limit models of \(N\) -player symmetric stochastic games, where players are exchangeable and symmetric entities. A number of papers have formally examined the connection between games with finitely many players and the corresponding limit model, including the works of [6]}, [7]}, [8]}. Given the ubiquity of large-scale decentralized systems in modern engineering, MFGs have been used to model a diverse range of applications, such resource management [9]}, [10]}, social conventions [11]}, power control in telecommunications networks [12]}, and traffic control [13]}, among many others.
